//   Copyright (c) 1999 CERN - European Organization for Nuclear Research.

//   Permission to use, copy, modify, distribute and sell this software
//   and its documentation for any purpose is hereby granted without fee,
//   provided that the above copyright notice appear in all copies and
//   that both that copyright notice and this permission notice appear in
//   supporting documentation. CERN makes no representations about the
//   suitability of this software for any purpose. It is provided "as is"
//   without expressed or implied warranty.
package ct25.xtreme.util;

import java.util.Arrays;

/*
 * Modified for Trove to use the java.util.Arrays sort/search
 * algorithms instead of those provided with colt.
 */

/**
 * Used to keep hash table capacities prime numbers.
 * Not of interest for users; only for implementors of hashtables.
 *
 * <p>Choosing prime numbers as hash table capacities is a good idea
 * to keep them working fast, particularly under hash table
 * expansions.
 *
 * <p>However, JDK 1.2, JGL 3.1 and many other toolkits do nothing to
 * keep capacities prime.  This class provides efficient means to
 * choose prime capacities.
 *
 * <p>Choosing a prime is <tt>O(log 300)</tt> (binary search in a list
 * of 300 ints).  Memory requirements: 1 KB static memory.
 *
 * @author wolfgang.hoschek@cern.ch
 * @version 1.0, 09/24/99
 */
public final class PrimeFinder {
	/**
	 * The largest prime this class can generate; currently equal to
	 * <tt>Integer.MAX_VALUE</tt>.
	 */
	public static final int LARGEST_PRIME = Integer.MAX_VALUE; //yes, it is prime.
	
	/**
	 * The prime number list consists of 11 chunks.
	 *
	 * Each chunk contains prime numbers.
	 *
	 * A chunk starts with a prime P1. The next element is a prime
	 * P2. P2 is the smallest prime for which holds: P2 >= 2*P1.
	 *
	 * The next element is P3, for which the same holds with respect
	 * to P2, and so on.
	 *
	 * Chunks are chosen such that for any desired capacity >= 1000
	 * the list includes a prime number <= desired capacity * 1.11.
	 *
	 * Therefore, primes can be retrieved which are quite close to any
	 * desired capacity, which in turn avoids wasting memory.
	 *
	 * For example, the list includes
	 * 1039,1117,1201,1277,1361,1439,1523,1597,1759,1907,2081.
	 *
	 * So if you need a prime >= 1040, you will find a prime <=
	 * 1040*1.11=1154.
	 *
	 * Chunks are chosen such that they are optimized for a hashtable
	 * growthfactor of 2.0;
	 *
	 * If your hashtable has such a growthfactor then, after initially
	 * "rounding to a prime" upon hashtable construction, it will
	 * later expand to prime capacities such that there exist no
	 * better primes.
	 *
	 * In total these are about 32*10=320 numbers -> 1 KB of static
	 * memory needed.
	 *
	 * If you are stingy, then delete every second or fourth chunk.
	 */
	
	private static final int[] PRIME_CAPACITIES = {
		//chunk #0
		LARGEST_PRIME,
		
		//chunk #1
		5,11,23,47,97,197,397,797,1597,3203,6421,12853,25717,51437,102877,205759,
		411527,823117,1646237,3292489,6584983,13169977,26339969,52679969,105359939,
		210719881,421439783,842879579,1685759167,
		
		//chunk #2
		433,877,1759,3527,7057,14143,28289,56591,113189,226379,452759,905551,1811107,
		3622219,7244441,14488931,28977863,57955739,115911563,231823147,463646329,927292699,
		1854585413,
		
		//chunk #3
		953,1907,3821,7643,15287,30577,61169,122347,244703,489407,978821,1957651,3915341,
		7830701,15661423,31322867,62645741,125291483,250582987,501165979,1002331963,
		2004663929,
		
		//chunk #4
		1039,2081,4177,8363,16729,33461,66923,133853,267713,535481,1070981,2141977,4283963,
		8567929,17135863,34271747,68543509,137087021,274174111,548348231,1096696463,
		
		//chunk #5
		31,67,137,277,557,1117,2237,4481,8963,17929,35863,71741,143483,286973,573953,
		1147921,2295859,4591721,9183457,18366923,36733847,73467739,146935499,293871013,
		587742049,1175484103,
		
		//chunk #6
		599,1201,2411,4831,9677,19373,38747,77509,155027,310081,620171,1240361,2480729,
		4961459,9922933,19845871,39691759,79383533,158767069,317534141,635068283,1270136683,
		
		//chunk #7
		311,631,1277,2557,5119,10243,20507,41017,82037,164089,328213,656429,1312867,
		2625761,5251529,10503061,21006137,42012281,84024581,168049163,336098327,672196673,
		1344393353,
		
		//chunk #8
		3,7,17,37,79,163,331,673,1361,2729,5471,10949,21911,43853,87719,175447,350899,
		701819,1403641,2807303,5614657,11229331,22458671,44917381,89834777,179669557,
		359339171,718678369,1437356741,
		
		//chunk #9
		43,89,179,359,719,1439,2879,5779,11579,23159,46327,92657,185323,370661,741337,
		1482707,2965421,5930887,11861791,23723597,47447201,94894427,189788857,379577741,
		759155483,1518310967,
		
		//chunk #10
		379,761,1523,3049,6101,12203,24407,48817,97649,195311,390647,781301,1562611,
		3125257,6250537,12501169,25002389,50004791,100009607,200019221,400038451,800076929,
		1600153859
	};
	
	static { //initializer
		// The above prime numbers are formatted for human readability.
		// To find numbers fast, we sort them once and for all.
		
		Arrays.sort(PRIME_CAPACITIES);
	}
	
	/**
	 * Returns a prime number which is <code>&gt;= desiredCapacity</code>
	 * and very close to <code>desiredCapacity</code> (within 11% if
	 * <code>desiredCapacity &gt;= 1000</code>).
	 *
	 * @param desiredCapacity the capacity desired by the user.
	 * @return the capacity which should be used for a hashtable.
	 */
	public static final int nextPrime(int desiredCapacity) {
		int i = Arrays.binarySearch(PRIME_CAPACITIES, desiredCapacity);
		if (i<0) {
			// desired capacity not found, choose next prime greater
			// than desired capacity
			i = -i -1; // remember the semantics of binarySearch...
		}
		return PRIME_CAPACITIES[i];
	}
}